{"paper":{"title":"On the Faithfulness of a Family of Representations of the Singular Braid Monoid $SM_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mohamad N. Nasser","submitted_at":"2024-05-08T08:37:38Z","abstract_excerpt":"For $n\\geq 2$, let $G_n$ be a group and let $\\rho: B_n\\rightarrow G_n$ be a representation of the braid group $B_n$. For a field $\\mathbb{K}$ and $a,b,c\\in \\mathbb{K}$, Bardakov, Chbili, and Kozlovskaya extend the representation $\\rho$ to a family of representations $\\Phi_{a,b,c}:SM_n \\rightarrow \\mathbb{K}[G_n]$ of the singular braid monoid $SM_n$, where $\\mathbb{K}[G_n]$ is the group algebra of $G_n$ over $\\mathbb{K}$. In this paper, we study the faithfulness of the family of representations $\\Phi_{a,b,c}$ in some cases. First, we find necessary and sufficient conditions of the families $\\Ph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04888","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.04888/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}